An analysis of the coupling of finite-element and Nyström methods in acoustic scattering

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Abstract
In this paper we analyze the use of a combined Nyström and finite-element procedure for approximating the scattered time-harmonic acoustic field produced when an incident wave interacts with a bounded inhomogeneity. The coupling technique uses a smooth artificial boundary and explicitly decouples the integral equation and finite-element computations. We prove convergence of the method. One highlight of this analysis is that we prove Sobolev space error estimates for the Nyström scheme (which is usually analyzed in Hölder spaces). We also present some numerical results.

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